Ax : (x is a unicorn) AND (x has a horn)
Which reads For All (A) x such that (:) x is a unicorn and x has a horn. In other words all unicorns have a horn.
Many things (x) have a horn, but none of them are unicorns. So we actually say this sentence is false. This solves the ontological problem that were we to agree that unicorns have a horn we are also implicitly suggesting that unicorns exist, which they do not.
Such a sentence also entails other statements such as:
-Ex : (x is a unicorn) AND -(x has a horn)
(where - means not)
reads: there does not exist x such that x is a unicorn and x does not have a horn.
So even if unicorns existed, if it doesn't have a horn it can't be a unicorn. Crude (since you might cut the horn off a unicorn) but for arguments sake let us assume all unicorns have horns for this piece of logic.
So our single statement actually says quite a lot. It means if we capture something with a horn, it may be a unicorn but is also says that if we capture something without a horn we know it is not a unicorn. We are immediately familiar with Unicorns and Not Unicorns.
We also know that the statement Ex : (x is a unicorn) AND -(x has a horn) is false. "If it is a unicorn and it doesn't have a horn" must be false.
So this means that were we to say of something X that it was a Unicorn and then say of Y that it didn't have a horn then X cannot be Y else we have a contradiction.
When I first learned Dialectics I initially argued that opposites have nothing in common. Something is either X xor it is Y you can't mix different things without getting contradictions. Black most definitely is not White.
But Logic is built on a "model of existence." We might call it the Discrete Model of Existence (DME). In this model things have absolute boundaries.
John Donne in his Meditation 17 might have a problem with this. "No man is an island" meaning that we are all connected and when one man dies we all lose something, just as an island loses something when even a clod of earth is washed into the sea.
Likewise the paradox of the Argo and many other problems have troubled proponents of the DME. In this paradox Jason and his Argonauts (meaning the sailors of the Argo) set off in a boat called the Argo. During their voyage every piece of timber is replaced at least once. So the question is what ship returned home. It can't be the Argo cos the Argo is wrecked in scraps of timber around the Black Sea, and if it isn't the Argo then Jason didn't return with any Argonauts. It is as though the Argo went through a slow ship wreck and a new ship was built. And however we think about it, even if the new ship is renamed the Argo at what points was the Old-Argo scrapped and the New-Argo launched? The point is it isn't discrete.
If we propose the Interconnected Model of Existence it solves all these problems. But we can no longer apply logic and contradictions so absolutely.
SO to take the classic of light and darkness. If there was never any darkness then when was the light switched on? There is actually no light in this world, cos it can never be switched on or off. Likewise if there was no light then where are the shadows in which to hide from it? There is actually no darkness. And what is bizarre is that a world with only light is indistinguishable from one where there is only darkness. Perhaps I stepped into the deep end there.
More simply consider a step ladder with its legs parted ready to be climbed. As we climb the step ladder it is worth remember that neither the side with steps on nor the supporting legs on the other side are enough to support our weight. The ladder works because the forces are balanced in the middle. If you remove one side it will collapse, and if you remove the other it will collapse also. The whole depends upon the unity of opposing forces. Now at no time is the force pushing one way the same as the other, it is because they are opposite forces that the step ladder stands up at all. This is an excellent example of opposing and quite separate things unifying in a balanced whole.
And the more you look at the world the more it is always in balance between opposing forces. Democratic politics is not stable because any particular party wins, but that the balance of power is shared between competing forces. This is the original meaning of dialectics in Ancient Greece: the search for truth through competing points of view in argument and dialogue. It is why Plato took up this form of writing.
The Yin Yang not only shows the coming together of opposing forces in a whole, but the fractal nature of this that within in opposing force is it dependence on the other opposing force. It is not that we can take a part of the whole and say well this at least is something, and it just happens to be in opposition to that other part. The deep realisation is that even this part owes its existence to what it opposes. When you push against a wall you see that the force the wall pushes back with is equal to your push, and it grows as you push. You are creating the opposing force as you push. This is the essence of our lives, our desires to push and move around the world creates the very forces that oppose our movement. In Daoism seeing the unity of the whole and the competing forces means that we do not get stuck on one side of the step ladder pushing aimlessly against the other. Just as the wall creates an opposing force as we push so the unenlightened create an ego which is either black or white and which sits on its side and directs are efforts against the wall, creating more and more counter forces until something yields and a new set of oppositions are created. But as the yin-yang shifts the ego leaping from one black to another white will always be in opposition to something. Being aware of these forces means we can escape the illusion of crude oppositions and be part of a much greater cosmic energy that exists beyond oppositions. People who add their weight behind war "efforts" are simply ignorant of this. Just like the step ladder the war exists only as long as people push on both sides. And when they stop pushing the war evaporates into nothing, like the force of the wall pushing against us when we stop. All these struggles come from no where and end up going no where.
So in Dialectics nothing exists "as an island" but always interconnected and in opposition to other things. One cannot say absolutely that something without a horn isn't a unicorn or be sure that something with a horn is a unicorn, it could after all be a horse with some surgery. In reality none of these entities exists absolutely and is fluid and changeable with other things. This is the source of magic and illusions as we are misdirected to think that one thing is really another. Yet DME persists in our thinking, perhaps because it is a neat short cut to using words which are discrete, and we are reluctant to let go of the idea that something or someone is exactly and only who they are. In Buddhism this resistance to allowing things to change and become what they are not, like the Argo, is the source of suffering and in personal existence is the illusion of Atta - the fixed discrete soul. In reality we are momentary and always changing, our boundaries and affiliations uncertain and in our heart there is no fixed identity. But that doesn't give us licence to be duplicitous and two-faced, lack integrity and be whimsical and uncommitted: on the contrary The Vow is the path to wisdom. Being straight and definite is the sign of a person who has stepped above the vagaries of conditional existence. The problem of Atta is when we confuse the changing with ourselves, when we allow our vows, intentions and purpose to be swayed by what is not us. In Hinduism this is taken to extremes with the story of Harishchandra who even keeps a vow that ultimately leads to executing his own wife. Perhaps I wonder in reality whether there was a more peaceful solution to his situation, rather than the dogged determination to remain strong in his vow. But in the story the gods who set the test up eventually felt pity for him and released him from his vow. But he did prove that he was not to be distracted by the uncertain dialectical world of opposing forces and change.
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